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Vortex Matter dynamics in a thin film of Nb with columnar indentations
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518 www.elsevier.com/locate/jmmm
Vortex Matter dynamics in a thin film of Nb with columnar indentations J.S. Nunesa,, R. Zadorosnya, A.A.M. Oliveiraa, C.M. Lepienskib, E.J. Patin˜oc,1, M.G. Blamirec, W.A. Ortiza a
Grupo de Supercondutividade e Magnetism, Departamento de Fı´sica, Universidade Federal de Sa˜o Carlos, Sa˜o Carlos, SP, Brazil b Departamento de Fı´sica, Universidade Federal do Parana´, Curitiba, PR, Brazil c Department of Materials Science, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Available online 23 February 2008
Abstract A superconducting film with columnar defects constitutes a rich scenario for studying Vortex Matter dynamics. This paper reports on the magnetic response of a 200 nm thick Nb film, pierced with a set of 900 columnar indentations of nearly triangular cross section, forming a square lattice. The column diameter is 1 mm and the distance between columns is 10 mm. To probe the interaction of Vortex Matter with the array of antidots, we have excited the sample with a significantly large AC-field, so that flux originally trapped by the columns could be unpinned and admitted into the superconducting sea surrounding the defects. The melting line of this system has a kink separating two different regimes, suggesting a crossover from the efficient pinning regime, at lower temperatures, to a temperatureinduced depinning. r 2008 Elsevier B.V. All rights reserved. PACS: 74.78.Db; 74.25.Ha; 74.25.Dw; 74.25.Qt Keywords: Superconductivity; Vortex Matter; Vortices; Melting line; Depinning; Columnar Defects
1. Introduction Vortex dynamics in a type-II superconductor can be substantially modified by pinning centers (PCs), whose presence affects the way a specific sample behaves in the presence of transport currents and applied magnetic fields. Depending on the type, strength, and density of PCs, the solid state phase of Vortex Matter can be modified, from a Bragg glass, for low densities of defects [1,2]; to a vortex glass, for uncorrelated PCs, like disorder or impurities [3,4]; to a Bose glass, when correlated disorder is present, as in the case of columnar defects (CDs) [5]. For each of those scenarios, the melting line (ML) separating the vortex-solid and vortex-liquid phases, exhibits a different behavior, which can be even used to identify the presence of a dominant class of PCs.
Corresponding author. Tel.: +55 16 3351 8228; fax: +55 16 3361 4835.
E-mail address: [email protected] (J.S. Nunes). Present address: Departamento de Fı´ sica, Universidad de los Andes, Cra. 1E No. 18A- 10. Edificio H.A.A. 4976, Bogota´ D.C., Colombia. 1
0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.02.097
Vinokur and coworkers [6,7] have studied the Bose-glass transition, anticipating that a temperature-induced depinning of the vortices, otherwise pinned by CDs, would occur at the lower-field, higher-temperature portion of the ML. This theoretical approach was used to successfully describe a two-regime solid–liquid frontier of the Vortex Matter phase diagram of an irradiated BSCCO sample containing CDs [8], for which, as in the model, a kink was clearly seen on the ML. The present work studies an Nb film containing a square array of CDs, whose ML also exhibits a kink, characteristic of the above discussed temperature-induced depinning. 2. Experimental procedure The superconducting system employed in this study is a 200 nm thick film of Nb, deposited on an Si (1 0 0) substrate, using a UHV DC-magnetron sputtering system in a chamber below 100 1C cooled with liquid nitrogen. Base pressure was better than 3 109 mbar, with a partial oxygen base pressure below 1011 mbar. A square array of
ARTICLE IN PRESS J.S. Nunes et al. / Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518
Fig. 1. Imaginary part of the AC-susceptibility of the indented Nb film at two different values of the applied field. Upper left: atomic force microscopy of a portion of the indented region.
900 indentations was pierced in the film, using an MTS Systems Nanoindenter XP. The arrangement covers an area of 300 mm 300 mm, with a lattice parameter d ¼ 10 mm. Each indentation has an effective diameter of 1 mm, and the distance between them is much larger than the typical scales of the superconducting phase, i.e., the coherence length and the London penetration depth (dbl, x), which means that there is enough space between columns to accommodate a fairly undistorted vortex lattice. As seen on the upper left panel of Fig. 1, the triangular empty column created by the nanoindenter tool is surrounded by damaged material, forming a nearly circular pinning region of continuously varying strength, where vortices are likely to be anchored. An informal correspondence might be set between this region and the irradiated spots of the BSCCO sample treated in Ref. [8]. To determine the ML we chose to measure the temperature dependence of the AC-susceptibility, wAC ¼ w0 +jw00 , using the peak temperature of the imaginary component as an indicator of the melting point. The validity of this choice has been extensively debated in the literature [9–11] and eventually agreed upon. However, in spite of its common use, other alternatives are also employed for this purpose, including measurements of the irreversibility line and of the third harmonic susceptibility, the latter being argued as the most adequate for studying the genuine ML of a clean, homogeneous material [12]. Magnetic measurements were conducted using the AC module of a Quantum Design SQUID Magnetometer MPMS-5S. 3. Results Fig. 1 shows typical experimental curves, taken with an excitation field amplitude h ¼ 1 Oe at the frequency
e517
f ¼ 100 Hz, illustrating how the peak in w00 evolves for different values of the applied field. As the imaginary part of the AC-susceptibility is associated with dynamical losses of the system, the peak temperature, Tp(H), corresponds to maximum dissipation, being thus associated with the increasing mobility that vortices experience during melting of the lattice. The upper left panel pictures a small portion of the array of CDs and a blowup of one indentation. In view of their large effective dimensions, the indentations constitute PCs of considerable strength, playing a major role on the arrangement of vortices in both solid and liquid states. One could then anticipate that, under such circumstances, probing vortex dynamics would require moderate-to-large excitations, what was confirmed experimentally by monitoring Tp for different values of h. A strong dependence was found, indicating that the peak temperature for this system is, in fact, a function of applied and excitation fields, Tp(H,h). Fig. 2 shows three versions of the ML, taken with different values of the excitation field. For h ¼ 0.4 Oe the borderline seems monotonous, a behavior that transforms gradually into a two-regime frontier as h is increased up to 2 Oe. A kink develops at temperatures progressively lower and, if an analogy is made between the present system and the above-mentioned irradiated sample of BSCCO [8], the upper temperature portion of the ML is associated with the depinning crossover predicted by Vinokur and others [6,7] for systems with CDs. The upper right inset shows how Tp varies with h at H=12 kOe; the same results are shown as a horizontal row of stars at the upper left of the HT-diagram. Details of the fittings to the ML taken with h=2 Oe are shown in Fig. 3. The high-field, low-temperature region is adjusted using a power law, as derived in the scaling theory by Nelson and Vinokur [5], whereas the remaining of the line is clearly dominated by an expression of the form T2 exp(T/T0), which describes the temperature-induced
Fig. 2. Three versions of the ML for different values of h. The upper right panel presents the peak temperature for different values of h, at 12 kOe. The same data are also presented as stars at the upper left. The upper critical field, Hc2, is shown for reference.
ARTICLE IN PRESS e518
J.S. Nunes et al. / Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518
depinning, the melting point is forced to occur at lower temperatures (or lower fields, for isothermal processes) and the Bose-glass transition becomes impractical. In summary, we have used the peak temperature of the imaginary susceptibility as an indicator of the melting point of a vortex solid, obtaining at different version of the ML for each value of the excitation field. We argue that, although apparently artificial, this is an expected characteristic of the studied system, resulting from the considerable strength of the PCs, so that an additional aid, coming from the excitation field, is necessary to unpin vortices otherwise anchored around the extended CDs. Acknowledgments
Fig. 3. ML taken with h ¼ 2 Oe: crossover from a Bose-glass melting to a temperature-induced depinning. Fittings from different regimes are discussed in the text.
The authors acknowledge financial support from Brazilian agencies FAPESP, CAPES, and CNPq. References
depinning, predicted by Vinokur and coworkers [6,7] for a system containing CDs. 4. Final remarks The observed dependence of the ML on h is not to be taken as an experimental artifact but, on the contrary, as a confirmation that, above Tkink, the frontier between the solid and liquid phases is strongly affected by additional mobility of unpinned vortices, what is facilitated by excitations of larger magnitude. Due to thermally induced
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
T. Giamarchi, P. Le Doussal, Phys. Rev. B 52 (1995) 1242. T. Giamarchi, P. Le Doussal, Phys. Rev. B 55 (1997) 6577. M.P.A. Fisher, Phys. Rev. Lett. 62 (1989) 1415. D.S. Fisher, et al., Phys. Rev. B 43 (1991) 130. D.R. Nelson, V.M. Vinokur, Phys. Rev. B 48 (1993) 13060. A.V. Lopatin, V.M. Vinokur, Phys. Rev. Lett. 92 (2004) 067008. J. Kierfeld, V.M. Vinokur, Phys. Rev. Lett. 94 (2005) 077005. S.S. Banerjee, et al., Phys. Rev. Lett. 90 (2003) 087004. L. Krusin-Elbaum, et al., Phys. Rev. Lett. 72 (1994) 1914. A.V. Samoilov, et al., Phys. Rev. Lett. 75 (1995) 186. L. Krusin-Elbaum, et al., Phys. Rev. Lett. 75 (1995) 187. See, for instance, A.A.M. Oliveira, P.N. Lisboa-Filho, W.A. Ortiz, this volume.
Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518 www.elsevier.com/locate/jmmm
Vortex Matter dynamics in a thin film of Nb with columnar indentations J.S. Nunesa,, R. Zadorosnya, A.A.M. Oliveiraa, C.M. Lepienskib, E.J. Patin˜oc,1, M.G. Blamirec, W.A. Ortiza a
Grupo de Supercondutividade e Magnetism, Departamento de Fı´sica, Universidade Federal de Sa˜o Carlos, Sa˜o Carlos, SP, Brazil b Departamento de Fı´sica, Universidade Federal do Parana´, Curitiba, PR, Brazil c Department of Materials Science, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Available online 23 February 2008
Abstract A superconducting film with columnar defects constitutes a rich scenario for studying Vortex Matter dynamics. This paper reports on the magnetic response of a 200 nm thick Nb film, pierced with a set of 900 columnar indentations of nearly triangular cross section, forming a square lattice. The column diameter is 1 mm and the distance between columns is 10 mm. To probe the interaction of Vortex Matter with the array of antidots, we have excited the sample with a significantly large AC-field, so that flux originally trapped by the columns could be unpinned and admitted into the superconducting sea surrounding the defects. The melting line of this system has a kink separating two different regimes, suggesting a crossover from the efficient pinning regime, at lower temperatures, to a temperatureinduced depinning. r 2008 Elsevier B.V. All rights reserved. PACS: 74.78.Db; 74.25.Ha; 74.25.Dw; 74.25.Qt Keywords: Superconductivity; Vortex Matter; Vortices; Melting line; Depinning; Columnar Defects
1. Introduction Vortex dynamics in a type-II superconductor can be substantially modified by pinning centers (PCs), whose presence affects the way a specific sample behaves in the presence of transport currents and applied magnetic fields. Depending on the type, strength, and density of PCs, the solid state phase of Vortex Matter can be modified, from a Bragg glass, for low densities of defects [1,2]; to a vortex glass, for uncorrelated PCs, like disorder or impurities [3,4]; to a Bose glass, when correlated disorder is present, as in the case of columnar defects (CDs) [5]. For each of those scenarios, the melting line (ML) separating the vortex-solid and vortex-liquid phases, exhibits a different behavior, which can be even used to identify the presence of a dominant class of PCs.
Corresponding author. Tel.: +55 16 3351 8228; fax: +55 16 3361 4835.
E-mail address: [email protected] (J.S. Nunes). Present address: Departamento de Fı´ sica, Universidad de los Andes, Cra. 1E No. 18A- 10. Edificio H.A.A. 4976, Bogota´ D.C., Colombia. 1
0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.02.097
Vinokur and coworkers [6,7] have studied the Bose-glass transition, anticipating that a temperature-induced depinning of the vortices, otherwise pinned by CDs, would occur at the lower-field, higher-temperature portion of the ML. This theoretical approach was used to successfully describe a two-regime solid–liquid frontier of the Vortex Matter phase diagram of an irradiated BSCCO sample containing CDs [8], for which, as in the model, a kink was clearly seen on the ML. The present work studies an Nb film containing a square array of CDs, whose ML also exhibits a kink, characteristic of the above discussed temperature-induced depinning. 2. Experimental procedure The superconducting system employed in this study is a 200 nm thick film of Nb, deposited on an Si (1 0 0) substrate, using a UHV DC-magnetron sputtering system in a chamber below 100 1C cooled with liquid nitrogen. Base pressure was better than 3 109 mbar, with a partial oxygen base pressure below 1011 mbar. A square array of
ARTICLE IN PRESS J.S. Nunes et al. / Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518
Fig. 1. Imaginary part of the AC-susceptibility of the indented Nb film at two different values of the applied field. Upper left: atomic force microscopy of a portion of the indented region.
900 indentations was pierced in the film, using an MTS Systems Nanoindenter XP. The arrangement covers an area of 300 mm 300 mm, with a lattice parameter d ¼ 10 mm. Each indentation has an effective diameter of 1 mm, and the distance between them is much larger than the typical scales of the superconducting phase, i.e., the coherence length and the London penetration depth (dbl, x), which means that there is enough space between columns to accommodate a fairly undistorted vortex lattice. As seen on the upper left panel of Fig. 1, the triangular empty column created by the nanoindenter tool is surrounded by damaged material, forming a nearly circular pinning region of continuously varying strength, where vortices are likely to be anchored. An informal correspondence might be set between this region and the irradiated spots of the BSCCO sample treated in Ref. [8]. To determine the ML we chose to measure the temperature dependence of the AC-susceptibility, wAC ¼ w0 +jw00 , using the peak temperature of the imaginary component as an indicator of the melting point. The validity of this choice has been extensively debated in the literature [9–11] and eventually agreed upon. However, in spite of its common use, other alternatives are also employed for this purpose, including measurements of the irreversibility line and of the third harmonic susceptibility, the latter being argued as the most adequate for studying the genuine ML of a clean, homogeneous material [12]. Magnetic measurements were conducted using the AC module of a Quantum Design SQUID Magnetometer MPMS-5S. 3. Results Fig. 1 shows typical experimental curves, taken with an excitation field amplitude h ¼ 1 Oe at the frequency
e517
f ¼ 100 Hz, illustrating how the peak in w00 evolves for different values of the applied field. As the imaginary part of the AC-susceptibility is associated with dynamical losses of the system, the peak temperature, Tp(H), corresponds to maximum dissipation, being thus associated with the increasing mobility that vortices experience during melting of the lattice. The upper left panel pictures a small portion of the array of CDs and a blowup of one indentation. In view of their large effective dimensions, the indentations constitute PCs of considerable strength, playing a major role on the arrangement of vortices in both solid and liquid states. One could then anticipate that, under such circumstances, probing vortex dynamics would require moderate-to-large excitations, what was confirmed experimentally by monitoring Tp for different values of h. A strong dependence was found, indicating that the peak temperature for this system is, in fact, a function of applied and excitation fields, Tp(H,h). Fig. 2 shows three versions of the ML, taken with different values of the excitation field. For h ¼ 0.4 Oe the borderline seems monotonous, a behavior that transforms gradually into a two-regime frontier as h is increased up to 2 Oe. A kink develops at temperatures progressively lower and, if an analogy is made between the present system and the above-mentioned irradiated sample of BSCCO [8], the upper temperature portion of the ML is associated with the depinning crossover predicted by Vinokur and others [6,7] for systems with CDs. The upper right inset shows how Tp varies with h at H=12 kOe; the same results are shown as a horizontal row of stars at the upper left of the HT-diagram. Details of the fittings to the ML taken with h=2 Oe are shown in Fig. 3. The high-field, low-temperature region is adjusted using a power law, as derived in the scaling theory by Nelson and Vinokur [5], whereas the remaining of the line is clearly dominated by an expression of the form T2 exp(T/T0), which describes the temperature-induced
Fig. 2. Three versions of the ML for different values of h. The upper right panel presents the peak temperature for different values of h, at 12 kOe. The same data are also presented as stars at the upper left. The upper critical field, Hc2, is shown for reference.
ARTICLE IN PRESS e518
J.S. Nunes et al. / Journal of Magnetism and Magnetic Materials 320 (2008) e516–e518
depinning, the melting point is forced to occur at lower temperatures (or lower fields, for isothermal processes) and the Bose-glass transition becomes impractical. In summary, we have used the peak temperature of the imaginary susceptibility as an indicator of the melting point of a vortex solid, obtaining at different version of the ML for each value of the excitation field. We argue that, although apparently artificial, this is an expected characteristic of the studied system, resulting from the considerable strength of the PCs, so that an additional aid, coming from the excitation field, is necessary to unpin vortices otherwise anchored around the extended CDs. Acknowledgments
Fig. 3. ML taken with h ¼ 2 Oe: crossover from a Bose-glass melting to a temperature-induced depinning. Fittings from different regimes are discussed in the text.
The authors acknowledge financial support from Brazilian agencies FAPESP, CAPES, and CNPq. References
depinning, predicted by Vinokur and coworkers [6,7] for a system containing CDs. 4. Final remarks The observed dependence of the ML on h is not to be taken as an experimental artifact but, on the contrary, as a confirmation that, above Tkink, the frontier between the solid and liquid phases is strongly affected by additional mobility of unpinned vortices, what is facilitated by excitations of larger magnitude. Due to thermally induced
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
T. Giamarchi, P. Le Doussal, Phys. Rev. B 52 (1995) 1242. T. Giamarchi, P. Le Doussal, Phys. Rev. B 55 (1997) 6577. M.P.A. Fisher, Phys. Rev. Lett. 62 (1989) 1415. D.S. Fisher, et al., Phys. Rev. B 43 (1991) 130. D.R. Nelson, V.M. Vinokur, Phys. Rev. B 48 (1993) 13060. A.V. Lopatin, V.M. Vinokur, Phys. Rev. Lett. 92 (2004) 067008. J. Kierfeld, V.M. Vinokur, Phys. Rev. Lett. 94 (2005) 077005. S.S. Banerjee, et al., Phys. Rev. Lett. 90 (2003) 087004. L. Krusin-Elbaum, et al., Phys. Rev. Lett. 72 (1994) 1914. A.V. Samoilov, et al., Phys. Rev. Lett. 75 (1995) 186. L. Krusin-Elbaum, et al., Phys. Rev. Lett. 75 (1995) 187. See, for instance, A.A.M. Oliveira, P.N. Lisboa-Filho, W.A. Ortiz, this volume.